Conceptualization of electronic dose to water for dosimetry in external beam radiotherapy

This study conceptualizes electronic dose to water, which is the radiation energy imparted to a unit mass of water by electronic interactions. The new dosimetry framework excludes nuclear interactions and consequently associated corrections and uncertainties from conventional dosimetry. Based on the international code of practice for dosimetry in radiotherapy, the procedures to determine electronic doses were formulated for high-energy photon, electron, proton, and ion beams. Nitrogen-based water-equivalent gas (WEG) mixtures were designed for use in gas-sealed ionization chambers for proton and ion beams. The proposed procedures were tested in a thought experiment and demonstrated compatibility with conventional absorbed dose for photon and electron beams and improved accuracy for proton and ion beams. The dosimetric uncertainty will be reduced from \SI{1.4}{%} to \SI{1.3}{%} for proton beams and from \SI{2.4}{%} to \SI{1.9}{%} for ion beams. With WEG ionization chambers, it will be further reduced to \SI{0.7}{%} for proton beams and \SI{1.0}{%} for ion beams. The new dose concept, electronic dose to water, can be readily used in radiotherapy practice and it will be medically more relevant than absorbed dose.

💡 Research Summary

The paper introduces a novel dosimetric quantity called “electronic dose to water” (De), defined as the radiation energy deposited per unit mass of water solely by electronic interactions. Conventional radiotherapy dosimetry relies on the absorbed dose to water (D), which requires several correction factors—most notably the beam‑quality factor kQ/Q0, the mean energy expended per ion pair in air (Wair), and the water‑to‑air mass stopping‑power ratio (sw/air). These corrections become especially problematic for proton and ion beams because nuclear stopping contributes significantly to the energy deposition, leading to larger uncertainties (≈1.4 % for protons and 2.4 % for ions in the current IAEA code of practice).

By restricting the definition to electronic interactions only, De eliminates the Wair/Q0 term and the sw/air/Q0 term from the calibration equation. The resulting measurement equation (Eq. 6) is De = M ND (sew/air pch)Q/Q0, where M is the measured ionization charge, ND the calibration coefficient obtained with a 60 Co γ‑ray reference, sew/air the electronic stopping‑power ratio, and pch the chamber perturbation factor. For photon and electron beams, De is numerically identical to D because all deposited energy originates from electronic collisions. For protons and heavier ions, De provides a value that is free from the nuclear‑interaction‑related uncertainties that currently dominate the dose‑conversion chain.

To enable practical measurement of De with ionization chambers, the authors propose a “water‑equivalent gas” (WEG) mixture, primarily nitrogen‑based, whose electronic stopping power and mean excitation energy (I) match those of water. By satisfying IWEG = Iw, the β‑dependence of the electronic stopping‑power ratio cancels, making sew/weg a constant that can be removed from the calibration. Consequently, the measurement equation for a WEG‑filled chamber simplifies to De = M ND (pch)Q/Q0 (Eq. 8), i.e., only the chamber perturbation factor remains as a beam‑quality correction.

A thought experiment was performed using two Farmer‑type ionization chambers (one air‑filled, one WEG‑filled) calibrated with 60 Co γ‑rays. Various clinical beams—6 MV and 10 MV photons, 150 MeV protons, and 200 MeV/u carbon ions—were considered. Using the kQ/Q0 values from the IAEA code, the authors computed the relative standard uncertainties for conventional absorbed dose (ˆΔD) and for electronic dose measured with both air and WEG chambers (ˆΔDe). The results show that for photons and electrons the uncertainties remain at the level of the current standard (≈0.6 %). For protons, the uncertainty drops from 1.4 % to 1.3 % with an air‑filled chamber and further to 0.7 % with a WEG chamber. For ions, the reduction is from 2.4 % to 1.9 % (air) and to 1.0 % (WEG). These improvements stem directly from the removal of the sw/air and Wair uncertainties.

The paper also provides detailed designs for the WEG mixtures (Appendix A) and validates the theoretical assumptions about the cancellation of β‑dependence and the negligible impact of δ‑ray stopping‑power differences (Appendix B) through Monte‑Carlo simulations.

In summary, the authors present a coherent framework that retains the existing international calibration infrastructure while eliminating the nuclear‑interaction corrections that limit the accuracy of proton and ion dosimetry. The electronic dose to water can be measured with standard ionization chambers, and the use of a nitrogen‑based WEG further enhances precision. The approach promises immediate clinical applicability, though experimental validation of the gas mixtures, long‑term stability studies, and extension to heavier ion species remain necessary future steps.